After creating a loud media buzz about her outrageous – but apparently fictionalized – statements on Twitter, Scout Willis now has something people should be talking about: The girl can really sing.

Sporting a clean, blonde bob and a sleek, black spaghetti-strap dress, Willis, 20, the daughter of Bruce Willis and Demi Moore, took to the stage Thursday night as the lead vocalist in the band Gus + Scout at Manhattan's Rockwood Music Hall.

The other half of the duo is Willis's classmate at Brown, Gus Wenner, son of Rolling Stone founder Jann Wenner. No stranger to performing with Hollywood offspring, Wenner reportedly was in a band in 2009 with another Brown student, Steven Spielberg's daughter Sasha.

Rumer, who recently showed off her vocal prowess at the club, didn't seem nervous at all before her performance, according to an onlooker, and she greeted Kutcher as he arrived with a friend after midnight.

Willis, 23, attended the premiere of The Diary of Preston Plummer, where she cut a glamorous figure in a curve-hugging dress.

"It was fun making the movie and fascinating working with Robert Loggia," she told PEOPLE of starring alongside the longtime character actor in the film. "I wasn't in many scenes with him but it was cool being around so much wit and wisdom."

Rumer Willis wants to prove she has more than acting chops: the 23-year-old surprised the crowd at Jason Scoppa's Corzo Sessions inside Hollywood's Sayers Club by singing some soulful tunes – specifically Peggy Lee's "Fever" and "Valerie," made famous by Amy Winehouse. A guest at the show says the starlet was with a group of friends and was "calm, casual and cool." As for her performance? Says the source: "She was a great singer and was totally badass," adding that she requested to perform the second song after "Fever" went off without a hitch. "– Jennifer Garcia

 Rumer Willis stayed under the radar at the T-Mobile and Google Music-sponsored party at a private residence in the West Hollywood Hills. The starlet, who was recently in Europe, arrived at the bash (for Redlight Management) with two friends, but spent most of the night hanging out with Glee's Mark Sallling, who arrived earlier via taxi. The two chatted with each other all night, and their interactions seemed friendly, not romantic, says an observer, who noted that the two did leave the party together. – Dahvi Shira

Shortly before Demi Mooresplit with Ashton Kutcher, her previous husband Bruce Willis went to her house to ask her to get help for her worsening health, a source tells PEOPLE in this week's cover story.

"He was worried about her and wanted her to get better," says the source. "Many of her friends did the same thing, but she just wouldn't listen."

Willis, 56, is the father of their three daughters, two of whom – Rumer, 23, and Tallulah, 18 – are now staying with him while Moore, 49, seeks treatment. (Scout, 20, is away at college). Moore had been especially close to Rumer since the marriage collapse.

On Saturday night, Willis, 23 – who was apparently on hand when Moore's friends called 911 after the actress had an apparent seizure – stepped out for dinner at Comme Ça, joined by her friend Annie Starke, Annie's mother Glenn Close and Close's husband David Shaw.

As paramedics neared Demi Moore's front gate, one of the people on the line to 911 can be heard shouting out a name.

"Hey, Ru," says the man. "What's the name at the gate so that we can buzz them in from here?"

The dramatic emergency call for help last Monday night, after Moore went into convulsions when she "smoked something," never reveals more about "Ru's" identity, but this could be a reference to Moore's oldest daughter Rumer Willis.

Rumer, 23, goes by that nickname and uses it on her Twitter account. And it's Rumer who has most often been at her mother's side in the months since the actress's split from Ashton Kutcher, 33, after six years of marriage.